Details

Autor(en) / Beteiligte

• Durmus, Alain
• Moulines, Éric

Titel

NONASYMPTOTIC CONVERGENCE ANALYSIS FOR THE UNADJUSTED LANGEVIN ALGORITHM

Ist Teil von

• The Annals of applied probability, 2017-06, Vol.27 (3), p.1551-1587

Ort / Verlag

Hayward: Institute of Mathematical Statistics

Erscheinungsjahr

2017

Link zum Volltext

Quelle

Project Euclid_欧几里德项目期刊

Beschreibungen/Notizen

• In this paper, we study a method to sample from a target distribution π over ℝd having a positive density with respect to the Lebesgue measure, known up to a normalisation factor. This method is based on the Euler discretization of the overdamped Langevin stochastic differential equation associated with π. For both constant and decreasing step sizes in the Euler discretization, we obtain nonasymptotic bounds for the convergence to the target distribution π in total variation distance. A particular attention is paid to the dependency on the dimension d, to demonstrate the applicability of this method in the high-dimensional setting. These bounds improve and extend the results of Dalalyan.